It might be possible, but you can not control what the user has in the DB before activating your theme, so you might have to handle “quotes” which are not reviews in any case.
In theory you can try to detect based on the content, or if you use some specific meta values, based on them, whether it is a review or not and handle the html generation accordingly.
I would not be too worried about that as post format are rarely used, so the chance of them being used wrongly, is probably slim.
As for the not “dumb” at all part, You might be able to hack it, but the whole point of post formats is that it is standardized between themes. If you create something outside of the standard, it might work in your theme, but fail when the user switches to another, or fail integration with plugins, so not advisable at all.
It sounds like what you should consider is using a custom post type for it, which is what “testimonials” kind of plugins do.